Question

Show diagrammatically how forces of 7n and 9n combined to give a resultant force of 2n

Answer 1

Answer:

Given:

2 force have been provided such as 7N and 9N .

To find:

To get a net force of 2N and represent it in a diagram.

Concept:

Forces are vectors. Hence they have both magnitude and directions.

So we will try to first find out mathematically and then represent it in a diagram.

Calculation:

Let vector A be 9N and vector B be 7N.

Let them be located at an angle of 180° to one another. In other words , the vectors will be directed opposite to one another.

So resultant force as per Law of Vector Addition will be :

$| \vec r| = \sqrt{ { | \vec A| }^{2} + { | \vec B| }^{2} + 2 | \vec A| | \vec B| \cos( \theta) }$

Putting value of θ = 180°

$| \vec r| = \sqrt{ { | \vec A| }^{2} + { | \vec B| }^{2} + 2 | \vec A| | \vec B| \cos( 180 \degree) }$

We know that cos(180°) = -1

$| \vec r| = \sqrt{ { | \vec A| }^{2} + { | \vec B| }^{2} - 2 | \vec A| | \vec B| }$

$| \vec r| = \sqrt{{ \bigg\{ { | \vec A| }^{2} - { | \vec B| }^{2} \bigg\}} ^{2} }$

$| \vec r| = | \vec A| - | \vec B|$

$| \vec r| = 9 - 7 = 2 N$

So the vectors have to be kept at 180° to one another to get resultant as 2N.